Question

check whether the (5,-2), (6,4) and (7,-2) are the vertices of an isosceles triangle.

Answer 1

QUESTION :-

the (5,-2), (6,4) and (7,-2) are the vertices of an isosceles triangle.

SOLUTION:-

➩A(5,-2) =(x1,y1) : B(6,4)=(x2,y2) : C(7,-2)=(x3,y3)

here,

➩ apply distance formula ,

➩ AB =√(x2-x1)²-(y2-y1)²

➩ .°. AB = √(6-5)²-(4-(-2)²

➩ .°. AB=√1+36

➩.°. AB=√37

Again,

➩ apply distance formula ,

➩ AC =√(x3-x1)²-(y3-y1)²

➩ AC =√(7-5)²-(-2-(-2))²

➩ .°. AC = √4-0

➩ .°. AC=2

Again,

➩ apply distance formula ,

➩BC =√(x3-x2)²-(y3-y2)²

➩BC=√(7-6)²-(-2-4)²

➩ .°. BC = √(1²)+(-6)²

➩ .°. BC = √37

.°. AB=BC =√37

.°. hence, verified that the vertices are of an isosceles triangles.